Measurements of the midrapidity transverse energy distribution, $dEt/deta$, are presented for $p$$+$$p$, $d$$+$Au, and Au$+$Au collisions at $sqrt{s_{_{NN}}}=200$ GeV and additionally for Au$+$Au collisions at $sqrt{s_{_{NN}}}=62.4$ and 130 GeV. The $dEt/deta$ distributions are first compared with the number of nucleon participants $N_{rm part}$, number of binary collisions $N_{rm coll}$, and number of constituent-quark participants $N_{qp}$ calculated from a Glauber model based on the nuclear geometry. For Au$+$Au, $mean{dEt/deta}/N_{rm part}$ increases with $N_{rm part}$, while $mean{dEt/deta}/N_{qp}$ is approximately constant for all three energies. This indicates that the two component ansatz, $dE_{T}/deta propto (1-x) N_{rm part}/2 + x N_{rm coll}$, which has been used to represent $E_T$ distributions, is simply a proxy for $N_{qp}$, and that the $N_{rm coll}$ term does not represent a hard-scattering component in $E_T$ distributions. The $dE_{T}/deta$ distributions of Au$+$Au and $d$$+$Au are then calculated from the measured $p$$+$$p$ $E_T$ distribution using two models that both reproduce the Au$+$Au data. However, while the number-of-constituent-quark-participant model agrees well with the $d$$+$Au data, the additive-quark model does not.
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